The "my" is the possessive pronoun so if I said "In my zoo" I would be talking about a zoo that I owned. It's most common to hear "At the zoo" for example "there are tigers at the zoo" or "I am at the zoo". To say "There are tigers in the zoo" would not be wrong but it is less common. To say "I am in the zoo" sounds quite odd so I would stick to "at the zoo". Hope this helps :)

She works at the zoo (job) but Wild animals are well cared for in the zoo (place) No?